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Revista Matemática Iberoamericana


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Volume 14, Issue 1, 1998, pp. 47–61
DOI: 10.4171/RMI/233

Published online: 1998-04-30

A proof of the smoothing properties of the positive part of Boltzmann's kernel

François Bouchut[1] and Laurent Desvillettes[2]

(1) Ecole Normale Superieure, Paris, France
(2) CMLA-ENS, Cachan, France

We give two direct proofs of Sobolev estimates for the positive part of Boltzmanns kernel. The first deals with a cross section with separated variables; no derivative is needed in this case. The second is concerned with a general cross section having one derivative in the angular variable.

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Bouchut François, Desvillettes Laurent: A proof of the smoothing properties of the positive part of Boltzmann's kernel. Rev. Mat. Iberoam. 14 (1998), 47-61. doi: 10.4171/RMI/233